Search results for: interpolation method

Authors: R.Vinodha S. Abraham Lincoln, J. Prakash

Abstract:

Multi-loop (De-centralized) Proportional-Integral- Derivative (PID) controllers have been used extensively in process industries due to their simple structure for control of multivariable processes. The objective of this work is to design multiple-model adaptive multi-loop PID strategy (Multiple Model Adaptive-PID) and neural network based multi-loop PID strategy (Neural Net Adaptive-PID) for the control of multivariable system. The first method combines the output of multiple linear PID controllers, each describing process dynamics at a specific level of operation. The global output is an interpolation of the individual multi-loop PID controller outputs weighted based on the current value of the measured process variable. In the second method, neural network is used to calculate the PID controller parameters based on the scheduling variable that corresponds to major shift in the process dynamics. The proposed control schemes are simple in structure with less computational complexity. The effectiveness of the proposed control schemes have been demonstrated on the CSTR process, which exhibits dynamic non-linearity.

Keywords: Multiple-model Adaptive PID controller, Multivariableprocess, CSTR process.

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Authors: X. Z. Gao, S. J. Ovaska, X. Wang

Abstract:

Prediction of sinusoidal signals with time-varying frequencies has been an important research topic in power electronics systems. To solve this problem, we propose a new fuzzy predictive filtering scheme, which is based on a Finite Impulse Response (FIR) filter bank. Fuzzy logic is introduced here to provide appropriate interpolation of individual filter outputs. Therefore, instead of regular 'hard' switching, our method has the advantageous 'soft' switching among different filters. Simulation comparisons between the fuzzy predictive filtering and conventional filter bank-based approach are made to demonstrate that the new scheme can achieve an enhanced prediction performance for slowly changing sinusoidal input signals.

Keywords: Predictive filtering, fuzzy logic, sinusoidal signals, time-varying frequencies.

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Authors: Suresh Sahu, Abhijeet M. Vaidya, Naresh K. Maheshwari

Abstract:

The efforts to understand the heat transfer behavior of supercritical water in supercritical water cooled reactor (SCWR) are ongoing worldwide to fulfill the future energy demand. The higher thermal efficiency of these reactors compared to a conventional nuclear reactor is one of the driving forces for attracting the attention of nuclear scientists. In this work, a solution procedure has been described for solving supercritical fluid flow problems in complex geometries. The solution procedure is based on non-staggered grid. All governing equations are discretized by finite volume method (FVM) in curvilinear coordinate system. Convective terms are discretized by first-order upwind scheme and central difference approximation has been used to discretize the diffusive parts. k-ε turbulence model with standard wall function has been employed. SIMPLE solution procedure has been implemented for the curvilinear coordinate system. Based on this solution method, 3-D Computational Fluid Dynamics (CFD) code has been developed. In order to demonstrate the capability of this CFD code in supercritical fluid flows, heat transfer to supercritical water in circular tubes has been considered as a test problem. Results obtained by code have been compared with experimental results reported in literature.

Keywords: Curvilinear coordinate, body-fitted mesh, momentum interpolation, non-staggered grid, supercritical fluids.

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Authors: Mehran Yazdi, Luc Beaulieu

Abstract:

Artifact is one of the most important factors in degrading the CT image quality and plays an important role in diagnostic accuracy. In this paper, some artifacts typically appear in Spiral CT are introduced. The different factors such as patient, equipment and interpolation algorithm which cause the artifacts are discussed and new developments and image processing algorithms to prevent or reduce them are presented.

Keywords: CT artifacts, Spiral CT, Artifact removal.

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Authors: A. Pashayev, R. Sadiqov, C. Ardil, F. Ildiz , H. Karabork

Abstract:

The new technology of fuzzy neural networks for identification of parameters for mathematical models of geofields is proposed and checked. The effectiveness of that soft computing technology is demonstrated, especially in the early stage of modeling, when the information is uncertain and limited.

Keywords: Identification, interpolation methods, neuro-fuzzy networks, geofield.

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Authors: Dimitris Varsamis, Nicholas Karampetakis

Abstract:

It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: Bivariate interpolation polynomial, Polynomial basis, Transformations.

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Authors: Andrei A. Kolyshkin

Abstract:

In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

Keywords: Numerical methods, "Mathematica", e-learning.

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Authors: Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong

Abstract:

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

Keywords: Multiclass classification, feed-forward backpropagation neural network, interval neutrosophic sets, uncertainty.

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Authors: Uzma Bashir, Jamaludin Md. Ali

Abstract:

This study is concerned with the visualization of monotone data using a piecewise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and othertwo are leftfree. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves.

Keywords: Trigonometric splines, Monotone data, Shape preserving, C1 monotone interpolant.

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Authors: S. Kulsri, M. Jaroensutasinee, K. Jaroensutasinee

Abstract:

We developed a new method based on quasimolecular modeling to simulate the cavity flow in three cavity shapes: rectangular, half-circular and bucket beer in cgs units. Each quasi-molecule was a group of particles that interacted in a fashion entirely analogous to classical Newtonian molecular interactions. When a cavity flow was simulated, the instantaneous velocity vector fields were obtained by using an inverse distance weighted interpolation method. In all three cavity shapes, fluid motion was rotated counter-clockwise. The velocity vector fields of the three cavity shapes showed a primary vortex located near the upstream corners at time t ~ 0.500 s, t ~ 0.450 s and t ~ 0.350 s, respectively. The configurational kinetic energy of the cavities increased as time increased until the kinetic energy reached a maximum at time t ~ 0.02 s and, then, the kinetic energy decreased as time increased. The rectangular cavity system showed the lowest kinetic energy, while the half-circular cavity system showed the highest kinetic energy. The kinetic energy of rectangular, beer bucket and half-circular cavities fluctuated about stable average values 35.62 x 103, 38.04 x 103 and 40.80 x 103 ergs/particle, respectively. This indicated that the half-circular shapes were the most suitable shape for a shrimp pond because the water in shrimp pond flows best when we compared with rectangular and beer bucket shape.

Keywords: Quasi-molecular modelling, particle modelling, lid driven cavity flow.

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Authors: R .Lassoued, M. Guenfoud

Abstract:

An accurate procedure to determine free vibrations of beams and plates is presented. The natural frequencies are exact solutions of governing vibration equations witch load to a nonlinear homogeny system. The bilinear and linear structures considered simulate a bridge. The dynamic behavior of this one is analyzed by using the theory of the orthotropic plate simply supported on two sides and free on the two others. The plate can be excited by a convoy of constant or harmonic loads. The determination of the dynamic response of the structures considered requires knowledge of the free frequencies and the shape modes of vibrations. Our work is in this context. Indeed, we are interested to develop a self-consistent calculation of the Eigen frequencies. The formulation is based on the determination of the solution of the differential equations of vibrations. The boundary conditions corresponding to the shape modes permit to lead to a homogeneous system. Determination of the noncommonplace solutions of this system led to a nonlinear problem in Eigen frequencies. We thus, develop a computer code for the determination of the eigenvalues. It is based on a method of bisection with interpolation whose precision reaches 10 -12. Moreover, to determine the corresponding modes, the calculation algorithm that we develop uses the method of Gauss with a partial optimization of the "pivots" combined with an inverse power procedure. The Eigen frequencies of a plate simply supported along two opposite sides while considering the two other free sides are thus analyzed. The results could be generalized with the case of a beam by regarding it as a plate with low width. We give, in this paper, some examples of treated cases. The comparison with results presented in the literature is completely satisfactory.

Keywords: Free frequencies, beams, rectangular plates.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

Abstract:

The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: M. Alauddin, M. A. Ullah, M. Alom, M. N. Islam

Abstract:

The rivers in Bangladesh are highly unstable having loose boundaries, mild slope of water surface and bed, irregular siltation of huge sediment coming from upstream, among others. The groins are installed in the river bank to deflect the flowing water away from the vulnerable zones. The conventional groins are found to be unstable and ineffective. The combined groin having both impermeable and permeable components in the same structure improves the flow field to function better over others. The main goal of this study is to analyze the hydraulic characteristics induced by the combined groins of different alignments by using a 2D numerical model, iRIC Nays2DH. In this numerical simulation, the K-ε model for turbulence and Cubic Interpolation Pseudo-particle (CIP) method for advective terms are utilized. A particular flow condition is applied in the channel for all sets of groins with different alignments. The simulation results reveal that the combined groins alter the flow patterns considerably, with no significant recirculation of flow in the groin field. The effect of different alignments of groins is found somewhat different. Based on hydraulic features caused by the groins, the combined groin that aligns the permeable component towards slightly downstream performs better over others.

Keywords: Combined groin, alignment, hydraulic characteristics, numerical model.

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Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

Abstract:

This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: Kinematics, degree of freedom, optimization, robot manipulator.

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Authors: R.Marsalek

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (ν ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ν <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: ferro-precipitate, adsorption, SDS, zeta potential

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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Authors: Dimitrios N. Gkritzapis, Elias E. Panagiotopoulos, Dionissios P. Margaris, Dimitrios G. Papanikas

Abstract:

A full six degrees of freedom (6-DOF) flight dynamics model is proposed for the accurate prediction of short and long-range trajectories of high spin and fin-stabilized projectiles via atmospheric flight to final impact point. The projectiles is assumed to be both rigid (non-flexible), and rotationally symmetric about its spin axis launched at low and high pitch angles. The mathematical model is based on the full equations of motion set up in the no-roll body reference frame and is integrated numerically from given initial conditions at the firing site. The projectiles maneuvering motion depends on the most significant force and moment variations, in addition to wind and gravity. The computational flight analysis takes into consideration the Mach number and total angle of attack effects by means of the variable aerodynamic coefficients. For the purposes of the present work, linear interpolation has been applied from the tabulated database of McCoy-s book. The developed computational method gives satisfactory agreement with published data of verified experiments and computational codes on atmospheric projectile trajectory analysis for various initial firing flight conditions.

Keywords: Constant-Variable aerodynamic coefficients, low and high pitch angles, wind.

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Authors: Mahsa Tavakoli, Seyed Mohammad Hojjati, Yahya Kooch

Abstract:

In this study, the effect of coal mining activities on lead and cadmium concentrations and distribution in soil was investigated in Hyrcanian forest, North Iran. 16 plots (20×20 m²) were established by systematic-randomly (60×60 m²) in an area of 4 ha (200×200 m²-mine entrance placed at center). An area adjacent to the mine was not affected by the mining activity; considered as the controlled area. In order to investigate soil lead and cadmium concentration, one sample was taken from the 0-10 cm in each plot. To study the spatial pattern of soil properties and lead and cadmium concentrations in the mining area, an area of 80×80m² (the mine as the center) was considered and 80 soil samples were systematic-randomly taken (10 m intervals). Geostatistical analysis was performed via Kriging method and GS⁺ software (version 5.1). In order to estimate the impact of coal mining activities on soil quality, pollution index was measured. Lead and cadmium concentrations were significantly higher in mine area (Pb: 10.97±0.30, Cd: 184.47±6.26 mg.kg^-1) in comparison to control area (Pb: 9.42±0.17, Cd: 131.71±15.77 mg.kg^-1). The mean values of the PI index indicate that Pb (1.16) and Cd (1.77) presented slightly polluted. Results of the NIPI index showed that Pb (1.44) and Cd (2.52) presented slight pollution and moderate pollution respectively. Results of variography and kriging method showed that it is possible to prepare interpolation maps of lead and cadmium around the mining areas in Hyrcanian forest. According to results of pollution and risk assessments, forest soil was contaminated by heavy metals (lead and cadmium); therefore, using reclamation and remediation techniques in these areas is necessary.

Keywords: Traditional coal mining, heavy metals, pollution indicators, geostatistics, caspian forest.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Ampon Dhamacharoen, Kanittha Chompuvised

Abstract:

In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.

Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Z. Veselý, M. Honner

Abstract:

High power laser – total emissivity method (HPL-TE method) for determination of coatings relative total emissivity dependent on the temperature is introduced. Method principle, experimental and evaluation parts of the method are described. Computer model of HPL-TE method is employed to perform the sensitivity analysis of the effect of method parameters on the sample surface temperature in the positions where the surface temperature and radiation heat flux are measured.

Keywords: High temperature laser testing, measurement ofthermal properties, emissivity, coatings.

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Authors: Ibrahim Abu-Alshaikh

Abstract:

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

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Authors: Wenlong Liu, Yucheng Liu

Abstract:

This paper introduces the application of seismic wave method in earthquake prediction and early estimation. The advantages of the seismic wave method over the traditional earthquake prediction method are demonstrated. An example is presented in this study to show the accuracy and efficiency of using the seismic wave method in predicting a medium-sized earthquake swarm occurred in Wencheng, Zhejiang, China. By applying this method, correct predictions were made on the day after this earthquake swarm started and the day the maximum earthquake occurred, which provided scientific bases for governmental decision-making.

Keywords: earthquake prediction, earthquake swarm, seismicactivity method, seismic wave method, Wencheng earthquake

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Authors: Foad Saadi, M. Jalali Azizpour, S.A. Zahedi

Abstract:

The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.

Keywords: Variational Iteration Method (VIM), HomotopyPerturbation Method (HPM), Homotopy Analysis Method (HAM), KdV Equation.

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Authors: Guangbin Wang, Deyu Sun, Fuping Tan

Abstract:

In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.

Keywords: preconditioned, MAOR method, linear system, convergence, comparison.

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Authors: Marrick Neri, Esmeraldo Ronnie Rey Zara

Abstract:

In this paper, we apply a semismooth active set method to image inpainting. The method exploits primal and dual features of a proposed regularized total variation model, following after the technique presented in [4]. Numerical results show that the method is fast and efficient in inpainting sufficiently thin domains.

Keywords: Active set method, image inpainting, total variation model.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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